Problem: Simplify the following expression: $ p = \dfrac{-5}{6} - \dfrac{1}{6x - 10} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6x - 10}{6x - 10}$ $ \dfrac{-5}{6} \times \dfrac{6x - 10}{6x - 10} = \dfrac{-30x + 50}{36x - 60} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{1}{6x - 10} \times \dfrac{6}{6} = \dfrac{6}{36x - 60} $ Therefore $ p = \dfrac{-30x + 50}{36x - 60} - \dfrac{6}{36x - 60} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-30x + 50 - 6 }{36x - 60} $ Distribute the negative sign: $p = \dfrac{-30x + 50 - 6}{36x - 60}$ $p = \dfrac{-30x + 44}{36x - 60}$ Simplify the expression by dividing the numerator and denominator by 2: $p = \dfrac{-15x + 22}{18x - 30}$